'Most people conclude it's Looney Tunes time when Ed's around," says Edward Aczel halfway through his show. Spoken by any other comic, that would sound entirely credible. But spoken by Aczel, it's ridiculous – because Aczel is (after a fashion) the least funny comic on the fringe. Forget jokes, timing and technique: Aczel serves up rumpled, shuffling, semi-audible comedy. It's a bit like an end-of-year report delivered by a middle manager whose staff have left for the pub.

This is anti-comedy, a cultish subsection of fringe standup, with Aczel, Neil Hamburger and Count Arthur Strong as its leading lights. These comics get their laughs by being so-bad-they're-good: hubristic incompetents whose desire to perform comedy is matched only by their lack of ability. But what's funny about not being funny? And how can we tell a brilliant anti-comic from a plain old unfunny one?

"I've always liked comics who are inclined to be a shambles," says Aczel, 43. "And I like to accentuate that part of myself. The reality is, I don't think I could ever pull off being a high-status comedian. Quick jokes and ruling the roost – I've never thought I could pull that off."

The anti-comedy shtick, he says, is just 21st-century clowning. Chaplin and Mr Bean pretended to be incapable, too. But their brand of ineptitude was in keeping with a theatrical style. Aczel's hypernaturalistic, downbeat-bordering-on-catatonic approach is new. The same principles apply, though, apparently. "People like the underdog," he says. "They like watching people struggle through badly. That's the natural order of things in comedy."

Don't you alienate as many people as you amuse? At the Reading festival last year, after all, Hamburger stepped out in front of a crowd who weren't in on the anti-joke, and was booed off the stage. "You just have to get the crowd to buy into it," says Aczel, "and then they'll be quite happy. Yes, you can have bad anti-comedians who don't bring people in. But if you can make being unfunny funny, it'll make people laugh."

Despite their wildly differing politics, John Malkovich and Harold Pinter were friends. Now the film star is directing Julian Sands in a tribute to the playwright. As the Edinburgh festival launches, Stephen Moss meets them